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- Title
Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms.
- Authors
Li, Yanlin; Khan, Meraj Ali; Aquib, MD; Al-Dayel, Ibrahim; Youssef, Maged Zakaria
- Abstract
In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen–Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Additionally, we explore the minimality of Lagrangian submanifolds in locally metallic product space forms, and we apply the result to create a classification theorem for isotropic submanifolds whose mean curvature is constant. More specifically, we have demonstrated that the submanifolds are either a product of two Einstein manifolds with Einstein constants, or they are isometric to a totally geodesic submanifold. To support our findings, we provide several examples.
- Subjects
SUBMANIFOLDS; EINSTEIN manifolds; GEODESICS
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 3, p183
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13030183